Journal ArticleDOI
Compression of individual sequences via variable-rate coding
Jacob Ziv,A. Lempel +1 more
TLDR
The proposed concept of compressibility is shown to play a role analogous to that of entropy in classical information theory where one deals with probabilistic ensembles of sequences rather than with individual sequences.Abstract:
Compressibility of individual sequences by the class of generalized finite-state information-lossless encoders is investigated. These encoders can operate in a variable-rate mode as well as a fixed-rate one, and they allow for any finite-state scheme of variable-length-to-variable-length coding. For every individual infinite sequence x a quantity \rho(x) is defined, called the compressibility of x , which is shown to be the asymptotically attainable lower bound on the compression ratio that can be achieved for x by any finite-state encoder. This is demonstrated by means of a constructive coding theorem and its converse that, apart from their asymptotic significance, also provide useful performance criteria for finite and practical data-compression tasks. The proposed concept of compressibility is also shown to play a role analogous to that of entropy in classical information theory where one deals with probabilistic ensembles of sequences rather than with individual sequences. While the definition of \rho(x) allows a different machine for each different sequence to be compressed, the constructive coding theorem leads to a universal algorithm that is asymptotically optimal for all sequences.read more
Citations
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Journal ArticleDOI
A parallel architecture for high-speed data compression
James A. Storer,John H. Reif +1 more
TL;DR: This work presents a massively parallel architecture for textual substitution that is based on a systolic pipe of 3839 identical processing elements that forms what is essentially an associative memory for strings that can “learn” new strings on the basis of the text processed thus far.
Patent
Sort order preserving method for data storage compression
TL;DR: A method for data compression of records in storage that offers the decoding speed of variable-to-fixed codes without loss of sort order characteristics when stored in coded form was proposed in this article.
Journal ArticleDOI
A comparison of index-based lempel-Ziv LZ77 factorization algorithms
Anisa Al-Hafeedh,Maxime Crochemore,Lucian Ilie,Evguenia Kopylova,William F. Smyth,German Tischler,Munina Yusufu +6 more
TL;DR: An overview of several recent algorithms proposed that extend the usefulness of LZ factorization, for example, to the calculation of maximal repetitions and their efficiency in terms of time and space is provided.
Journal ArticleDOI
Optimal Rule Caching and Lossy Compression for Longest Prefix Matching
Ori Rottenstreich,Janos Tapolcai +1 more
TL;DR: This paper studies the applicability of rule caching and lossy compression to create packet classifiers requiring much less memory than the theoretical size limits of the semantically-equivalent representations, enabling significant reduction in their cost and power consumption.
Proceedings ArticleDOI
Resolution of the Burrows-Wheeler Transform Conjecture
Dominik Kempa,Tomasz Kociumaka +1 more
TL;DR: This paper shows that r=\mathcal{O}(z\log^{2}n)$ holds for every text, and proves that many results related to BWT automatically apply to methods based on LZ77, and implies the first non-trivial relation between the number of runs in the BWT of the text and its reverse.
References
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Book
Information Theory and Reliable Communication
TL;DR: This chapter discusses Coding for Discrete Sources, Techniques for Coding and Decoding, and Source Coding with a Fidelity Criterion.
Journal ArticleDOI
A universal algorithm for sequential data compression
Jacob Ziv,A. Lempel +1 more
TL;DR: The compression ratio achieved by the proposed universal code uniformly approaches the lower bounds on the compression ratios attainable by block-to-variable codes and variable- to-block codes designed to match a completely specified source.
Journal ArticleDOI
On the Complexity of Finite Sequences
A. Lempel,Jacob Ziv +1 more
TL;DR: A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented, related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated.
Journal ArticleDOI
Coding theorems for individual sequences
TL;DR: The finite-state complexity of a sequence plays a role similar to that of entropy in classical information theory (which deals with probabilistic ensembles of sequences rather than an individual sequence).
Journal ArticleDOI
On Information Lossless Automata of Finite Order
TL;DR: The application of the tests to finite deterministic automata is discussed and a method of constructing a decoder for a given finite automaton that is information lossless of finite order, is described.